Vilenkin, B., Chikatunov, V.I. and Pavlíček, T. 2009: The pattern of species turnover resulting from stochastic population dynamics: The model and field data. Ecological Modelling 220: 657-661.

The model of random population dynamics in a sampling site returns geometric distribution of longevities of continuous presence (=persistence) and Poisson distribution of the presence–absence transitions. This discrete-time stochastic process describes the presence–absence pattern observed in the beetles surveyed 6 years on Mount Carmel, Israel. Homogeneous pools of species mostly on the Families rank, exhibit the predicted by the model patterns. Conformity to an ergodic hypothesis is the criterion of ecological homogeneity. This criterion assumes the equivalence of short-term behavior of entire pool and longterm behavior of any species from this pool. The pool of all 801 species of Order Coleoptera does not match the model. Thus a taxon of an arbitrary rank may not be considered a priory as a unit of ecological study. Determined from field data parameters of the model are biased and magnitude of the bias depends on longevity of the survey. Parameter of distribution depends also on species tolerance, which is the level adaptation of given species to given environment in given time interval. Random process of species turnover may be considered as a game of species to gain their presence against deteriorative fluctuations of environmental conditions.